| Summary: | In this paper, we investigate the energy-efficient resource allocation in two-tier massive multiple-input multiple-output (mMIMO) heterogeneous networks with wireless backhaul. Millimeter wave frequency is adopted at the mMIMO macro base station (MBS), and the cellular frequency is considered at small cell BS with orthogonal frequency-division multiple access. To lower the hardware cost and energy consumption at the MBS, two hybrid analog/digital precoding schemes are proposed according to the connectivity, i.e., fully connected and subarray structures. In order to design the small cell cluster-based power and subchannel allocation, we aim to maximize the energy efficiency of the system with limited wireless backhaul and users' quality of service constraints. The formulated problem is non-convex mixed integer nonlinear fraction programming, which is non-trivial to solve directly. By exploiting fractional programming, we propose a two-loop iterative resource allocation algorithm to solve the nonconvex problem. Specifically, integer relaxation and a Dinkelback method are considered to transform the outer loop problem into a difference of convex programming (DCP). Following this, the first-order Taylor approximation is considered to linearize this inner loop DCP problem into a convex optimization framework. Lagrange dual problem is considered to obtain the closed-form power allocation. Furthermore, we prove the convergence of the proposed iterative algorithm. Numerical results are provided to validate our proposed schemes.
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